Self-Organized States in Cellular Automata: Exact Solution

The spatial structure, fluctuations as well as all state probabilities of self-organized (steady) states of cellular automata can be found (almost) exactly and {\em explicitly} from their Markovian dynamics. The method is shown on an example of a natural sand pile model with a gradient threshold.Comment: 4 pages (REVTeX), incl. 2 figures (PostScript

Abelian Sandpile Model on the Honeycomb Lattice

We check the universality properties of the two-dimensional Abelian sandpile model by computing some of its properties on the honeycomb lattice. Exact expressions for unit height correlation functions in presence of boundaries and for different boundary conditions are derived. Also, we study the statistics of the boundaries of avalanche waves by using the theory of SLE and suggest that these curves are conformally invariant and described by SLE2.Comment: 24 pages, 5 figure

Infinite volume limit of the Abelian sandpile model in dimensions d >= 3

We study the Abelian sandpile model on Z^d. In dimensions at least 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit mu of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure mu, and study ergodic properties of this process. The main techniques we use are a connection between the statistics of waves and uniform two-component spanning trees and results on the uniform spanning tree measure on Z^d.Comment: First version: LaTeX; 29 pages. Revised version: LaTeX; 29 pages. The main result of the paper has been extended to all dimensions at least 3, with a new and simplyfied proof of finiteness of the two-component spanning tree. Second revision: LaTeX; 32 page

Fine Structure of Avalanches in the Abelian Sandpile Model

We study the two-dimensional Abelian Sandpile Model on a square lattice of linear size L. We introduce the notion of avalanche's fine structure and compare the behavior of avalanches and waves of toppling. We show that according to the degree of complexity in the fine structure of avalanches, which is a direct consequence of the intricate superposition of the boundaries of successive waves, avalanches fall into two different categories. We propose scaling ans\"{a}tz for these avalanche types and verify them numerically. We find that while the first type of avalanches has a simple scaling behavior, the second (complex) type is characterized by an avalanche-size dependent scaling exponent. This provides a framework within which one can understand the failure of a consistent scaling behavior in this model.Comment: 10 page

Частица со спином 1 в цилиндрическом базисе: метод проективных операторов

In this paper, the system of equations describing a spin 1 particle is studied in cylindric coordinates with the use of tetrad formalism and the matrix 10-dimension formalism of Duffin – Kemmer – Petieau. After separating the variables, we apply the method proposed by Fedorov – Gronskiy and based on the use of projective operators to resolve the system of 10 equations in the r variable. In the presence of an external uniform magnetic field, we construct in an explicit form three independent classes of wave functions with corresponding energy spectra. Separately the massless field with spin 1 is studied; there are found four linearly independent solutions, two of which are gauge ones, and other two do not contain gauge degrees of freedom. Meanwhile, the method of Fedorov – Gronskiy is also used.В настоящей работе система уравнений, описывающая частицу со спином 1, изучается в цилиндрических координатах с использованием тетрадного формализма и матричного 10-мерного формализма Даффина – Кеммера – Петье. После разделения переменных для решения системы 10 уравнений относительно переменной применяется метод, предложенный Федоровым – Гронским и основанный на применении проективных операторов. При наличии внешнего однородного магнитного поля построены в явном виде три независимых класса волновых функций с соответствующими энергетическими спектрами. Отдельно исследуется безмассовое поле со спином 1; найдено четыре линейно независимых решения, два из которых калибровочные, а остальные два не содержат калибровочных степеней свободы. При этом также используется метод Федорова – Гронского

Палладий-полимерный нанокомпозит: эффективный катализатор зеленых процессов кросссочетания по Сузуки–Мияуре и восстановления нитробензола по Мотт-Шотки

A new catalyst for green Suzuki–Miyaura cross-coupling and Mott-Schottky nitrobenzene reduction processes was prepared by thermolysis of palladium (II) poly-5-vinyltetrazolate. Heterogeneous catalyst includes Pd-nanoparticles supported on polymeric matrix. It presents recoverable and recyclable catalyst and the catalyzed reactions proceed in aqueous media at room temperature in aerobic conditions.Посредством термолиза поли-5-винилтетразолата палладия(II) был получен новый катализатор для зеленых процессов кросс-сочетания Сузуки–Мияуры и восстановления нитробензола по Мотт-Шотки. Гетерогенный катализатор содержит наночастицы Pd, стабилизированные полимерной матрицей. Данный катализатор является легко восстанавливаемым и пригодным для повторного использования, а также катализирует реакции, проводимые в водной среде при комнатной температуре в аэробных условиях

Neutron and synchrotron X-ray powder study of copper(II) chloride complex with deuterated 1-ethyltetrazole

The structure of the copper(II) chloride complex with deuterated 1-ethyltetrazole has been investigated in the temperature range of 2-290 K using neutron and synchrotron X-ray powder diffraction. The compound was found to exhibit structural transformation at ca 180 K, without change of space group and main structural motif. At higher temperatures, the complex reveals positional disorder of the ethyl group, whereas no disorder is observed at lower temperatures. Temperature dependence of the lattice parameters, obtained from synchrotron X-ray data, showed main lattice changes at the transformation, explained by structural features of the complex. From the magnetic measurements, the effect of the disorder on paramagnetic behaviour of the compound was found. Detailed structural data of the compound at 2 and 290 K, obtained from neutron powder diffraction data, are reported. © by Oldenbourg Wissenschaftsverlag, München